In:
Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 654 ( 2010-07-10), p. 207-231
Abstract:
We study the modulational instability of geophysical Rossby and plasma drift waves within the Charney–Hasegawa–Mima (CHM) model both theoretically, using truncated (four-mode and three-mode) models, and numerically, using direct simulations of CHM equation in the Fourier space. We review the linear theory of Gill ( Geophys. Fluid Dyn. , vol. 6, 1974, p. 29) and extend it to show that for strong primary waves the most unstable modes are perpendicular to the primary wave, which correspond to generation of a zonal flow if the primary wave is purely meridional. For weak waves, the maximum growth occurs for off-zonal inclined modulations that are close to being in three-wave resonance with the primary wave. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the nonlinear jet pinching predicted by Manin & Nazarenko ( Phys. Fluids , vol. 6, 1994, p. 1158). We find that, for strong primary waves, these narrow zonal jets further roll up into Kármán-like vortex streets, and at this moment the truncated models fail. For weak primary waves, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominate primary wave, so that the truncated description holds for longer. The two-dimensional vortex streets appear to be more stable than purely one-dimensional zonal jets, and their zonal-averaged speed can reach amplitudes much stronger than is allowed by the Rayleigh–Kuo instability criterion for the one-dimensional case. In the long term, the system transitions to turbulence helped by the vortex-pairing instability (for strong waves) and the resonant wave–wave interactions (for weak waves).
Type of Medium:
Online Resource
ISSN:
0022-1120
,
1469-7645
DOI:
10.1017/S0022112010000510
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2010
detail.hit.zdb_id:
1472346-3
detail.hit.zdb_id:
218334-1
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